In the art of synthesizing signals, three distinguishable techniques have been used: direct analog synthesis, indirect analog synthesis, and direct digital synthesis.
In the direct analog synthesis technique, the desired signal is produced by combining and mixing various combinations of signals derived from multiplying and dividing a reference frequency signal. In synthesizing a signal having a wide frequency range, this direct technique becomes extremely complex and costly because of the many components required for the multiplying-dividing and mixing-combining processes. Hence this technique is not widely used for synthesizing signals in either the high frequency or wide frequency ranges.
In indirect analog synthesis, phase lock loops with programmable frequency dividers are commonly used to synthesize a signal with the desired frequencies. This technique is by far the most widely used at present in both commercial products and dedicated applications. The method owes its popularity in large part to the advent of inexpensive programmable frequency dividers in integrated circuit form. The result has been a substantial reduction in complexity, especially in comparison with direct analog synthesis.
Direct digital synthesis is useful for avoiding the above problems associated with analog syntheses. Basically, digital synthesis consists of generating a stream of points with digital logic circuits to represent a desired signal. Then this numerical data stream is converted into the actual desired signal by means of a k-bit digital-to-analog converter (DAC). The DAC output can be further processed to provide a more useful signal. For example, it can pass through a low pass filter for a smoother and cleaner signal and an amplifier for compensating losses incurred through the conversion and filtering processes. The resulting analog output is, ideally, free of sampling components. An example of such a system for synthesizing signals in the prior art is described in U.S. Pat. No. 3,928,813. FIG. 1 shows a diagram of one such typical digital numerical synthesizer known in the prior art. In this system, the defining relationship for frequency is: EQU F=(.DELTA..phi./.DELTA.T)/(2.pi.),
where .DELTA..phi. is the input phase increment for uniquely determining the frequency of the system output signal F and .DELTA.T is the period of the system digital clock, or 1/F.sub.clock, where F.sub.clock is the frequency of the system clock. In this system, 2.pi. is defined as 2.sup.M, where M is the number of bits in the field for .DELTA..phi., which ranges from 0 to 2.sup.M -1.
The basic system in FIG. 1 is easily modified to include phase modulation by adding in a phase modulation term, PM(T), at the phase accumulator output 101. Also, frequency modulation may be realized by adding in a carrier phase increment and a frequency modulation phase increment to form the instantaneous phase increment .DELTA..phi. 102. For a truly universal synthesizer, amplitude modulation may also be added to the system. For this implementation, a fast multiplier may be added at the sine table output 103. Other similar implementations for modulating the system output signal are described in U.S. Pat. No. 4,331,941.
The system in FIG. 1 may also be used as a fast switching frequency source. Such a usage of this circuit is quite common, because the circuit output 104 can change from F.sub.1 to F.sub.2 just by changing the carrier phase increment 102 from .DELTA..phi..sub.1 to .DELTA..phi..sub.2. Because of the complex multiplication and mixing processes associated with each switched frequency that need to be implemented, building a comparably fast switching analog-based synthesizer, however, would be very difficult.
A characteristic of the synthesizer of FIG. 1 is its phase continuity between adjacent output frequencies. In other words, the transition from a first frequency F.sub.1 to a second frequency F.sub.2 is accomplished without any abrupt carrier amplitude change. This lack of an abrupt change implies that no phase discontinuity occurs at the instant the system output signal switches from frequency F.sub.1 to frequency F.sub.2. To appreciate this phase continuous nature of the synthesizer output signal, one should consider the synthesizer represented by the phase ramps 201, 202, 203 in FIG. 2. The phase ramps 201, 202, 203 form an exemplary output of the phase accumulator 105 of FIG. 1 for three different carrier phase increments, .DELTA..phi. 102: .DELTA..phi..sub.1, .DELTA..phi..sub.2 and .DELTA..phi..sub.3. These carrier phase increments correspond to three output frequencies F.sub.1, F.sub.2 and F.sub.3, respectively. In FIG. 2, the phase at each frequency switch point 204 again changes without a discontinuity. In the time increment shown, T.sub.N, a total phase of 66.52 radians has accumulated. This amount is equivalent to approximately 10.5 cycles of a sine wave.
FIG. 3 shows the sine wave resulting from the signal represented by the phase accumulation in FIG. 2 passing through the sine-lookup ROM 106 and DAC 107 blocks of FIG. 1. The transition point for F.sub.1 to F.sub.2 301 and the one for F.sub.2 to F.sub.3 302, in keeping with the non-abrupt changes 204 in accumulated phase, are smooth and phase continuous.
The object of the present invention is not to preserve phase continuity but to allow frequency switching, or frequency hopping, with phase memory, among any number of frequencies F.sub.1, F.sub.2, F.sub.3, . . . , F.sub.N. In other words, with each frequency hop, the output signal assumes a new frequency at the same phase that the signal would have had if the signal had started with the new frequency at a common zero time, T.sub.0, when all the frequencies start at zero phase. Thus, the output of the signal in accordance with the present invention is equivalent to a signal resulting from switching among a series of separate oscillators having frequencies F.sub.1, F.sub.2, . . . , F.sub.N respectively, all of which start at time T.sub.0. FIG. 4 shows an example of such an equivalent analog system with phase memory. Three oscillators 401, 402, 403, which run continuously, are locked together to start simultaneously at T.sub.0. A switch 404 is used to select which oscillator is to be the output signal 405. Since all three oscillators 401, 402, 403 never stop, whenever the switch 404 selects a different source, the phase will seemingly jump to account for the current phase of the selected source. This system always has as its output 405 a source with its correct phase at the instant of switching. This ability of a system to maintain and remember a constant phase for each switched frequency as though each has started at a common starting time and be able to switch into any new frequency at the appropriate point of the constant phase is termed "phase memory." FIG. 5A shows the output signal of the system in FIG. 4 as it switches among F.sub.1, F.sub.2 and F.sub.3. The "glitch" 502 that occurs at the instant of switching 504 is characteristic of a frequency hopped source with phase memory.
FIG. 5B shows the phase term of the signal in FIG. 5A; it is analogous to the phase term in FIG. 2. The phase is composed of three different phase slopes 520, 522, 524. The first slope 520 starts at T=0 and corresponds to F.sub.1. The other two slopes 522, 524 correspond to F.sub.2 and F.sub.3. In fact, all three started their rise at T=0, but only one oscillator is sampled for an actual output at any given time. FIG. 5C illustrates the phase of all three oscillators simultaneously. FIG. 5B also shows the phase offsets P.sub.Cor1.fwdarw.2 526 and P.sub.Cor2.fwdarw.3 528 that exist when a frequency hop occurs from F.sub.1 to F.sub.2 and from F.sub.2 to F.sub.3, respectively; they are the cause of the abrupt change 502, or "glitch," during its frequency transition 504.
The prior art system in FIG. 1 may be modeled as a single oscillator that may be changed to a new frequency only by changing the value of the input phase increment .DELTA..phi. 102. The starting phase of the new frequency is just the ending phase of the one that preceded it. The present invention extends the system in FIG. 1 to appear that many oscillators are all running simultaneously and that only one is being sourced as the output at any given time. Since both phase memory and phase continuity are aspects of frequency hopping systems, one of the two is usually required and is determined by the exact application of the frequency hop.